Recognised as Dice notation
21d85
- 21d85
- 21 to 1785
- mean 903
- mode 903
Rolling 21d85 gives a total between 21 and 1,785, with a mean of 903 and a standard deviation of 112.4366. There are 32,945,601,421,837,202,492,154,701,709,747,314,453,125 equally likely ordered outcomes, and the most likely total is 903 at 0.352%.
The roll
Notation21d85
Dice21
Faces per die85
Minimum total21all 21 dice showing 1
Maximum total1,785all 21 dice showing 85
Distinct totals1,765
Mean903n(f + 1)/2 + modifier, exact
Variance12,642n(f² − 1)/12, exact
Standard deviation112.43664883≈
Counting the outcomes
Ordered outcomes32,945,601,421,837,202,492,154,701,709,747,314,453,12585^21, every die distinguishable
Most likely total903
Chance of that total0.352271%≈
Ways to roll it116,057,828,986,752,501,040,808,572,494,994,724,255exact count
Chance of the minimum3.03530656 × 10^-39%≈1 in 32,945,601,421,837,202,492,154,701,709,747,314,453,125
Chance of the maximum3.03530656 × 10^-39%≈1 in 32,945,601,421,837,202,492,154,701,709,747,314,453,125
Shape of the distribution
1,765 distinct totals, too many to list individually.
1st percentile643≈1.013% of rolls are this or lower
5th percentile718≈5.054% of rolls are this or lower
25th percentile827≈25.226% of rolls are this or lower
50th percentile903≈50.176% of rolls are this or lower
75th percentile979≈75.056% of rolls are this or lower
95th percentile1,088≈95.039% of rolls are this or lower
99th percentile1,163≈99.011% of rolls are this or lower
Chance of rolling at least
197100%≈
46299.9976%≈
90350.1761%≈
1,3440.0025%≈
1,6093.0041393 × 10^-11%≈
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